The primary objective in GAN applications in the machine learning
literature is to find solutions to this sample problem, or to `train'
the GAN. In statistical terminology, this corresponds to estimating
the GAN parameters \(\gamma \)  and \(\delta \) . (Of course, choosing the
parametric forms of the neural networks \(G(\cdot ,\cdot )\)  and \(D(\cdot ,\cdot )\) ,
or specifying the network architecture, is done before this.)
Devising algorithms that solve the sample
minimax problem (REF ) is very challenging and
a large body of machine learning literature on GANs focuses on this.
Discussions of convergence and stability of various GAN training algorithms
can be found for instance in [1]}, [2]},
and [3]}; more recent contributions include
[4]}, [5]}, and [6]}.
Another theoretical aspect of GANs studied in the machine learning
literature is how well the distribution of \(G(Z,\gamma )\)  can approximate
the target distribution of \(X\)  (e.g., [7]};
[8]}).
